Recently, it was also shown that the emergence of a rogue wave in the developed stage of supercontinuum generation (SCG) is also connected with MI [1]}. Mostly, the study of MI development in nonlinear optics was conducted using the basic nonlinear Schrödinger equation (NLSE). Though the analytic solution of the NLSE called the Akhmediev breather (AB) is existing for more than 30 years [2]}, and has the the ability to explains MI phenomena in nonlinear media, researchers in similar fields mostly used numerical approaches to investigate MI [3]}, [4]}. Recently, the analytic solution of an AB [2]} is being used for the analysis of the evolution of how a modulated continuous wave field transform into a train of ultrashort pulses [6]}, [7]}. In the same work, it was also shown how the AB provides insight into the initial phase of a continuous wave supercontinuum generation seeded by a noise-driven MI.
